The density profile of dark matter haloes with numerical simulation

Numerical simulations play important role in estimation of the LCDM (Lambda cold dark matter) model as the standard cosmological model in which dark matter and dark energy are the main driving force in the universe. It also helps us to understand the various properties of dark matter halo, especially the density profile in the haloes. In this article, we will review the progress on this issue since 1980s. By virtue of N-body simulation, we know that the density profiles of dark matter haloes are not exactly following a single power law as what the theoretical model predicted. Instead the power index of the density profile is gradually changing from -1 inside to -3 outside. Furthermore, the density profile is determined by halo's mass assembly history and the initial power spectrum of the cosmic density field. With efforts in the past forty years, we have known well the internal structure of haloes with mass greater than 10(6) solar mass, however we know less on that with mass less than this scale because of the limit of computational resources. In the second part of this article, we will review a highlight research on this issue recently. With a new multi-level zooming technic, Wang et al simulate the formation of present-day haloes over the full range of observed halo masses (20 orders of magnitude) in a cosmological framework. Here dark matter is assumed to be in the form of weakly interacting massive particles of mass approximately 100 GeV. This series of simulations help to resolve the internal structure of hundreds of Earth-mass haloes in as much detail as it does for hundreds of rich galaxy clusters. In this cosmic zoom simulation, the density profile over the whole mass range could be described by a two parameter fitting formulae very well. The concentration of these haloes gets decreased with the decreasing of the halo mass. An accurate fitting function for the mass concentration relation in the whole mass range is provided. With the knowledge of the density profile of all dark matter haloes, we could understand how the mass is distributed in the universe; how does the dark halo play a key role in the process of galaxy formation; and how to constrain the nature of the dark matter better with various astrophysical tools. However we need to admit that the impact of the baryon's complicated physics on halo's density profile is still an open question. This is still a challenge for us to fully understand the density profile of dark matter haloes finally, but this also means a chance in the forthcoming future in this field.